Finite Group Databasebeta

← #14823161

Subgroups — #14823161

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622501C211yesmaximal, characteristic
2#13072993C211yesmaximal, characteristic
3#13071639C211yesmaximal, characteristic
4#13069996C211yesmaximal, characteristic, complemented
5#13069946C211yesmaximal, characteristic, complemented
6#13069811C211yesmaximal, characteristic
7#13069625C211yesmaximal, characteristic
8#13069484C211yesmaximal, characteristic, complemented
9#13069256C211yesmaximal, characteristic, complemented
10#13069253C211yesmaximal, characteristic, complemented
11#13069228C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic, complemented
13#13068812C211yesmaximal, characteristic
14#13068515C211yesmaximal, characteristic, complemented
15C2×C11×#477C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C11×#477—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28#10622844—21no—
29#10622843—21no—
30#10622843C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38#10622603—21no—
39#10622603—21no—
40#10622600C2211yescharacteristic
41#10622599—21no—
42#10622591—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44C4⋊C4×Dic11C2211yescharacteristic
45#10622587C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49#10622553—21no—
50C4×(C2×D11)⋊C4C2211yescharacteristic
51C4×Dic11⋊C4—21no—
52#10622542C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622501—24no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—41no—
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#66999—22no—
79#66999—22no—
80C2×#4326—22no—
81C2×#4326—22no—
82C2×#4326—41no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66950—22no—
102#66950—41no—
103#66945—22no—
104#66945—41no—
105C11×#107—22no—
106C11×#107D414yes—
107C11×C4⋊C8—22no—
108C11×#103—22no—
109C11×#103—22no—
110#66899—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—22no—
125#66881—22no—
126#66880—22no—
127#66880—22no—
128#66879—22no—
129#66874—22no—
130#66872—22no—
131#66872—41no—
132#26810—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—42no—
140C2×Q8×C11—42no—
141C2×Q8×C11—81no—
142C2×Q8×C11#4112yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4C2×D412yes—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186#4326—44no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—42no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8#4112yes—
213C2×#485—111no—
214C2×#477D1111yescharacteristic, complemented
215#2492—111no—
216#2362—111no—
217#2066—111no—
218#2058—111no—
219#2035—111no—
220#2001—111no—
221#1971—111no—
222#1928—111no—
223#1927—111no—
224#1924—111no—
225#1878—111no—
226#1854—111no—
227#1776—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—84no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11#13712yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C4×D11—41no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290Dic22—41no—
291Dic22—41no—
292Dic22—41no—
293Dic22—41no—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16—111no—
299C2×C4⋊Q8C2×D1111yescharacteristic
300C2×C22⋊Q8—111no—
301C2×C22⋊Q8—111no—
302C2×C4×Q8C2×D1111yescharacteristic
303C2×#117—111no—
304#485—224no—
305#477—24no—
306C2×#107C2×D1111yescharacteristic
307C2×#107C2×D1111yescharacteristic
308C2×#106—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103C2×D1111yescharacteristic
317C2×#103C2×D1111yescharacteristic
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×#97—111no—
321#400—221no—
322#393—221no—
323#391—111no—
324#391—111no—
325#391—111no—
326#391—221no—
327#389—111no—
328#388—221no—
329#388—221no—
330#388—221no—
331#387—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—221no—
336C4×C22⋊C4—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#336—111no—
342#336—111no—
343C22×C11#52511yescharacteristic
344C22×C11D4211yescharacteristic
345C22×C11#54711yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57811yescharacteristic
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—81no—
363C4×C11#53211yescharacteristic
364C4×C11#54211yescharacteristic
365C4×C11#54811yescharacteristic
366C4×C11#55111yescharacteristic
367Dic11—41no—
368Dic11—41no—
369Dic11—42no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—21no—
375C22×Q8—111no—
376C22×Q8C22×D1111yescharacteristic
377C23×C4—111no—
378C2×Q16—222no—
379C2×Q16—222no—
380C2×Q16—441no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C4⋊Q8—22no—
386C4⋊Q8—41no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389C22⋊Q8—222no—
390C22⋊Q8—441no—
391C4×Q8—22no—
392C4×Q8—41no—
393#117—222no—
394#117—441no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C42—21no—
413C2×C42—111no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42C22×D1111yescharacteristic
418#107—22no—
419#107C22⋊D1114yes—
420#106—222no—
421#106—222no—
422#106—441no—
423C4⋊C8—22no—
424#103—22no—
425#103—22no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430C22⋊C8—222no—
431C22⋊C8—222no—
432#97—222no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445C2×C11#246111yescharacteristic
446C2×C11#311611yescharacteristic
447C2×C11#312111yescharacteristic
448C2×C11#326711yescharacteristic
449C2×C11#327011yescharacteristic
450C2×C11#334911yescharacteristic
451C2×C11#335611yescharacteristic
452D11—81no—
453C24—111no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—81no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8#434312yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—444no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8C2×C22⋊D1112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—112no—
509C4⋊C4—224no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4C2×C22⋊D1112yes—
518C4⋊C4C2×C22⋊D1112yes—
519C22⋊C4—224no—
520C22⋊C4—222no—
521C22⋊C4—441no—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C22⋊C4—881no—
525C42—21no—
526C42—21no—
527C42—42no—
528C42—221no—
529C42—221no—
530C42—442no—
531C42—442no—
532C42—881no—
533C11#2681011yescharacteristic, complemented, Sylow
534C23—221no—
535C23—221no—
536C23—221no—
537C23—221no—
538C23—221no—
539C23—221no—
540C23—221no—
541C23C2×D4×D1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546Q8—84no—
547Q8—441no—
548Q8—441no—
549Q8—441no—
550Q8—441no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4#6697112yes—
594C2×C4#6703711yescharacteristic
595C2×C4C2×#434311yescharacteristic
596C2×C4#6704011yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4C22×C22⋊D1111yescharacteristic
600C8—22no—
601C8—41no—
602C8—222no—
603C8—441no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22—441no—
608C22—441no—
609C22—441no—
610C22—441no—
611C22#1062315811yescharacteristic
612C22#1062316211yescharacteristic
613C22C2×#6697111yescharacteristic
614C22#1062329711yescharacteristic
615C22#1062330411yescharacteristic
616C22#1062330611yescharacteristic
617C22D4×C22⋊D1111yescharacteristic
618C4—22no—
619C4—41no—
620C4—42no—
621C4—42no—
622C4—42no—
623C4—81no—
624C4—441no—
625C4—441no—
626C4—441no—
627C4—442no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062316811yescharacteristic
632C4#1062317111yescharacteristic
633C4#1062334811yescharacteristic
634C4#1062336311yescharacteristic
635C2—881no—
636C2#1307259011yescharacteristic
637C2#1307878111yescharacteristic
638C2#1307885011yescharacteristic
639C2#1308013511yescharacteristic
640C2#1308018611yescharacteristic
641C2#1308114311yescharacteristic
642C2#1308123411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#477D11
hypocenterC11#26810
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #13069996C2semidirect
5. #13069946C2semidirect
8. #13069484C2semidirect
9. #13069256C2semidirect
10. #13069253C2semidirect
12. #13068957C2semidirect
14. #13068515C2semidirect
15. C2×C11×#477C2semidirect
214. C2×#477D11semidirect
533. C11#26810semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106225012
#130729932
#130716392
#130699962
#130699462
#130698112
#130696252
#130694842
#130692562
#130692532
#130692282
#130689572
#130688122
#130685152
C2×C11×#4772
#2681011